The prime factors of the number 720 are

Question

Accepted Answer

The prime factorization of a number involves expressing the number as a product of its prime factors. Let's break down the number 720 to understand why Option 4 is the correct answer.

### Explanation for Option 4:

1. **Prime Factorization of 720:**
   - Start by dividing 720 by the smallest prime number, which is 2:
     - $ 720 \div 2 = 360 $
     - $ 360 \div 2 = 180 $
     - $ 180 \div 2 = 90 $
     - $ 90 \div 2 = 45 $
   - Now, 45 is not divisible by 2, so move to the next smallest prime number, which is 3:
     - $ 45 \div 3 = 15 $
     - $ 15 \div 3 = 5 $
   - Finally, 5 is a prime number.

2. **Prime Factors:**
   - The complete prime factorization of 720 is $ 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5 $.

3. **Verification:**
   - Multiplying these prime factors gives:
     - $ 2^4 \times 3^2 \times 5 = 16 \times 9 \times 5 = 720 $.

Thus, Option 4 correctly lists the prime factors of 720 as $ 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5 $.

### Explanation for Why Other Options are Incorrect:

1. **Option 1: 2 × 2 × 3 × 3 × 2 × 5**
   - This option does not include enough factors of 2. It only includes three 2s, whereas the correct factorization requires four 2s.

2. **Option 2: 2 × 3 × 4 × 5 × 6**
   - This option includes composite numbers (4 and 6) instead of breaking them down into prime factors. The correct factorization should only include prime numbers.

3. **Option 3: 3 × 3 × 4 × 4 × 5**
   - This option incorrectly includes 4 as a factor, which is not a prime number. The correct factorization should only include prime numbers, and 4 should be broken down into $ 2 \times 2 $.

By following the prime factorization process, it is clear that Option 4 is the correct answer, as it accurately represents the prime factors of 720.